Table 1:

Estimated power from the proposed power calculations using a pilot study of size $n_0$ for varying sample sizes $n$. We assume the effect size under the alternative hypothesis is given by $\eta =1.4.\mathrm{\Delta }$ denotes the difference between the true value of the optimal regime and $B_0$ which is given by $\eta (1+\mathrm{\Delta })$, so $\mathrm{\Delta }=0$ corresponds to the true effect size being equal to $\eta$. The remaining columns display the mean, median, and standard deviation of the estimated powers across 500 simulated pilot studies as well as the true power which is calculated via simulation. We do not estimate the power for $n=250$ when the pilot is of size $n_0=400$, since it is implausible for the pilot sample size to exceed the full study sample size.

$\Delta$	$n$	$n_0$	True PWR	Mean PWR	Med PWR	SD PWR
0	250	200	0.42	0.54	0.54	0.32
0.25	250	200	0.99	0.96	0.99	0.09
0.5	250	200	1.00	1.00	1.00	0.01
0	500	200	0.83	0.77	0.92	0.30
0.25	500	200	1.00	0.99	1.00	0.04
0.5	500	200	1.00	1.00	1.00	0.00
0	750	200	0.98	0.84	0.99	0.27
0.25	750	200	1.00	1.00	1.00	0.02
0.5	750	200	1.00	1.00	1.00	0.00
0	500	400	0.82	0.77	0.85	0.24
0.25	500	400	1.00	1.00	1.00	0.01
0.5	500	400	1.00	1.00	1.00	0.00
0	750	400	0.98	0.89	0.98	0.19
0.25	750	400	1.00	1.00	1.00	0.00
0.5	750	400	1.00	1.00	1.00	0.00